How do we know stars are element factories?

In a nutshell, stars are mainly made of hygrogen, element 1.

over time, elements got more dense as they collided and cooled, leading to other gases, metals ...

then they explode, which lead to all kinds of further complex elements.

The stuff that makes up the universe a lot of it is from exploding star stuff, and the Earth was built up upon these remains and the atoms that make up organisms even could originally be from stars.